Problem: Solve for $x$ and $y$ using elimination. $\begin{align*}6x+3y &= -3 \\ 5x-3y &= -3\end{align*}$
Explanation: We can eliminate $y$ when its corresponding coefficients are negative inverses. Add the top and bottom equations. $11x = -6$ Divide both sides by $11$ and reduce as necessary. $x = -\dfrac{6}{11}$ Substitute $-\dfrac{6}{11}$ for $x$ in the top equation. $6( -\dfrac{6}{11})+3y = -3$ $-\dfrac{36}{11}+3y = -3$ $3y = \dfrac{3}{11}$ $y = \dfrac{1}{11}$ The solution is $\enspace x = -\dfrac{6}{11}, \enspace y = \dfrac{1}{11}$.